{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "We start by including the relevant libraries. One useful way to have data in python is with a numpy array. The probability for a die with N sides to come up with side n is 1/N if n<=N, else it is 0. Thus for k throws, the probability is 1/N^k if all numbers were possible, else it is 0." ] }, { "cell_type": "code", "execution_count": 122, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The 6 data points are [3 6 1 5 7 4]\n", "The highest throw gave the result 7\n", "The die has 1 side(s) with probability 0.0\n", "The die has 2 side(s) with probability 0.0\n", "The die has 3 side(s) with probability 0.0\n", "The die has 4 side(s) with probability 0.0\n", "The die has 5 side(s) with probability 0.0\n", "The die has 6 side(s) with probability 0.0\n", "The die has 7 side(s) with probability 0.258378156730653\n", "The die has 8 side(s) with probability 0.11595890717012251\n", "The die has 9 side(s) with probability 0.05719907150785242\n", "The die has 10 side(s) with probability 0.39517311289565976\n", "The die has 11 side(s) with probability 0.017158840006753703\n", "The die has 12 side(s) with probability 0.13234267594724544\n", "The die has 13 side(s) with probability 0.00629772832552616\n", "The die has 14 side(s) with probability 0.004037158698916453\n", "The die has 15 side(s) with probability 0.0026686798802703624\n", "The die has 16 side(s) with probability 0.0018118579245331643\n", "The die has 17 side(s) with probability 0.0012593617758774546\n", "The die has 18 side(s) with probability 0.000893735492310194\n", "The die has 19 side(s) with probability 0.0006461337552846464\n", "The die has 20 side(s) with probability 0.006174579888994684\n" ] } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import math\n", "import random\n", "data = np.array([3, 6, 1, 5, 7, 4]) # defines the data (the numbers of the throws)\n", "\n", "# The next lines can be used to instead simulate an experiment with an arbitrary die\n", "#data = np.zeros(20)\n", "#for i in range(0,np.size(data)):\n", "# data[i] = random.randint(1,13) # 13-sided die\n", "\n", "nDatapoints = np.size(data)\n", "print(\"The\" , nDatapoints , \"data points are \", data)\n", "\n", "# the priors represent out initial knowledge about the dice. Switch the comment to use equal prior probabilities instead\n", "priors = np.array([0, 0, 0.1/13, 0.1, 0.1/13, 0.5, 0.1/13, 0.1/13, 0.1/13, 0.1, 0.1/13, 0.1, 0.1/13, 0.1/13, 0.1/13, 0.1/13, 0.1/13, 0.1/13, 0.1/13, 0.1])\n", "#priors = np.ones(20)/20. # equal probability\n", "\n", "# the array \"sides\" just saves the number of sides corresponding to the dice,\n", "# so prior[i] belongs to a dice with sides[i] sides\n", "sides = priors*0\n", "for i in range(1, np.size(sides)+1):\n", " sides[i-1] = i\n", "posteriors = priors*0.\n", "\n", "\n", "#First do all steps at once; for this we need to find the largest element of the data array and compare it to\n", "#the number of sides on the die we consider\n", "largestElement = 0\n", "for i in data: # or use data.max()\n", " if i > largestElement:\n", " largestElement = i\n", "print(\"The highest throw gave the result\" , largestElement)\n", "# Calculate posteriors by multiplying with likelihood for numerator of Bayes' formula\n", "for i in range(0, np.size(sides)):\n", " if largestElement <= sides[i]:\n", " posteriors[i] = priors[i] / math.pow(sides[i], nDatapoints) # We multiply the prior by the likelihood,\n", " else: # meaning this calculates the numerator of Bayes' formula\n", " posteriors[i] = 0.\n", "# Now we calculate the denominator of Bayes' formula. This is just the normalization so all posterior\n", "norm = 0. # probabilities add up to 1\n", "for i in posteriors: # or use posteriors.sum()\n", " norm += i\n", "posteriors /= norm # divides all elements of the array by the constant\n", "# Now we can just output the results\n", "for i in range(0, np.size(sides)):\n", " print(\"The die has \", int(sides[i]), \" side(s) with probability \", posteriors[i])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now know all the posterior probabilities for all sides. But it would be nice to know how each indidivual number changes our knowledge. Also, we want some practice with plotting. For the second part to run, the first one has to be run already to fill the objects. For each single throw, we use as the prior the posterior from the previous step. Since Bayesian inference is consistent, thi will give us the exact same result in the end. One difficulty is how to save the information we get in Python so we can later plot it. Here the choice is to use a 2-d matrix, StepByStepPosteriors[j,i]. StepByStepPosteriors[j,i] gives the probability for a die with j sides after i datapoints are considered. i=0 is defined to be the prior." ] }, { "cell_type": "code", "execution_count": 123, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "\n", "# now the same, but step by step\n", "#StepByStepPosteriors = np.array(priors, ndmin=2)\n", "StepByStepPosteriors = np.zeros((np.size(priors), nDatapoints+1)) # Includes Priors as initial step\n", "\n", "for i in range(0, np.size(priors)): # Fill in the priors\n", " StepByStepPosteriors[i,0] = priors[i]\n", " \n", "# Now go through each step and multiply the previous probabilities (the priors for this step) with 1/N\n", "# or with 0 if the throw is imposible\n", "for i in range(1, nDatapoints+1):\n", " for j in range(0, np.size(priors)):\n", " if data[i-1] <= sides[j]:\n", " StepByStepPosteriors[j,i] = StepByStepPosteriors[j,i-1]/sides[j]\n", " else:\n", " StepByStepPosteriors[j,i] = 0\n", " # again, the denominator is a normalization\n", " norm = 0.\n", " for j in range(0, np.size(priors)):\n", " norm += StepByStepPosteriors[j,i]\n", " for j in range(0, np.size(priors)):\n", " StepByStepPosteriors[j,i] /= norm\n", " \n", "# The plot function takes a numpy array as input, but we have a matrix\n", "# In this case we make one numpy array for each possible die and save them\n", "# in a Python list\n", "\n", "steps = np.arange(nDatapoints+1) # This just makes an array 0, 1, ... to give the x-axis values of the\n", " # different steps\n", "plotpoints = [0] * np.size(priors) # this just initializes the list with the number of elements\n", "plt.figure(figsize=(15,10)) # this sets the size of the plot\n", "for i in range(2, np.size(priors)):\n", " plotpoints[i] = StepByStepPosteriors[i,:] # this is a way to get just one row or column from a matrix\n", " plt.plot(steps,plotpoints[i], label=\"d\"+str(i+1)) # The label is later used in the legend\n", "# Python automatically gives different line colors to the lines\n", "plt.ylabel('probability') # Always label the axes\n", "plt.xlabel('data point')\n", "plt.legend(loc='upper right')\n", "#plt.yscale('log') # this line switches from a plot linear in y to a log plot, can be toggeled\n", "\n", "# The next few lines are just there to plot the numbers from the throws on the tick marks\n", "tickmarks = [0]*(nDatapoints+1)\n", "tickmarks[0] = \"Prior\"\n", "for i in range(1, nDatapoints+1):\n", " tickmarks[i] = \"\\\"\"+str(int(data[i-1]))+\"\\\"\"\n", "plt.xticks(np.arange(nDatapoints+1), tickmarks)\n", "\n", "plt.rcParams.update({'font.size': 18}) # make the font bigger, so it is easier to read\n", "\n", "plt.xlim([0, nDatapoints+1.5]) # set the x-Axis range; make a bit of space for the legend on the right\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Modify the priors to see what happens if you have different information. For example: One dice of each type is in a bucket an drawn at random (equal probabilities for all). You can also try to use different data by modifying the array in the beginning." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }